a theoretical question on linear response function.

[chermisi]

Hi,
I have a theoretical question about the expression used by yambo to evaluate the response function.
I want to know if two mathematical expressions are equivalent, so I attach a pdf that contains these formula.
I want to calculate the real part of the response function at zero frequency and at different values of the transfer momentum.
However I get a real part of the response function monotonically increasing on increasing the transfer module, without any structure.
Moreover it seems to have a cuspid at the edge of the Brillouin zone.
Thanks
Daniele Chermisi PhD at Università di Roma "Sapienza"

[andrea marini]

Dear Daniele, to answer your question try to work out a little bit Eq.1 by rearranging the second fraction of Eq. 2 using a k-> -k and k-> (k+q) transformations. As long as your system is not perturbed by a time-dependent perturbation or by a magnetic field this transformation should be correct. Then switch from T-ordered quantities (Eq.2) to causal by changing the sign of the small damping in the second (or first ? I do not remember) fraction.

At this point you should easily (?) prove that Eq. 1 and Eq 3 are equivalent. I did not do the math myself but I think this is the case.

If you will not have success we will try to do the math.

Cheers

Andrea

[chermisi]

Dear Andrea,
Thank you very much for your promt reply, I will try to do the math and let you know.
Thanks
Daniele Chermisi

[chermisi]

I tried to do the replacement k->k-q, but I have problems with the occupation number.
In fact, for finite temperatures f(k1)-f(k2) is different from f(k1)(1-f(k2)).
Thanks
Daniele Chermisi PhD at Università di Roma "Sapienza"

[andrea marini]

Dear Daniele, at the moment I am in Trieste for a Yambo school. Please send me a private E-mail and I will try to help you as soon as I will be back in Rome.

Andrea

[andrea marini]

Daniele, please send me an E-mail. I am back in Rome and I can try to help you.

Andrea